Question

Given that there are five competitors for three seats in a car: Liam, Noah, William, Dale, and Mason. Liam and Noah must be together and William.

(a) William sits next to Dale
(b) Noah sits next to Mason
(c) Liam sits next to Noah
(d) Mason sits next to Liam

Answer 1

The question involves combinatorics and permutations to determine the possible arrangements of the competitors in the car. The correct answer is (c) Liam sits next to Noah.

Step-by-step explanation:

The subject of this question is mathematics, specifically combinatorics and permutations. To solve this problem, we can use the principle of permutations and combinations. Let's break it down step-by-step:

1. First, we know that Liam and Noah must sit together. We can treat them as a single entity, so we have 4 entities (Liam-Noah, William, Dale, and Mason) to arrange.
2. Now we need to consider the conditions: William sits next to Dale, Noah sits next to Mason, Liam sits next to Noah, and Mason sits next to Liam. Using these conditions, we can determine the possible positions of Liam-Noah and then arrange the remaining entities around them.
3. There are 2 possible positions for Liam-Noah: either Liam is on the left and Noah is on the right, or Noah is on the left and Liam is on the right.
4. If we consider Liam on the left and Noah on the right, the possible arrangements of entities are: (Liam-Noah, William, Dale, Mason) and (Liam-Noah, William, Mason, Dale).
5. If we consider Noah on the left and Liam on the right, the possible arrangements of entities are: (Noah-Liam, William, Dale, Mason) and (Noah-Liam, William, Mason, Dale).
6. Therefore, there are a total of 4 possible arrangements: (Liam-Noah, William, Dale, Mason), (Liam-Noah, William, Mason, Dale), (Noah-Liam, William, Dale, Mason), and (Noah-Liam, William, Mason, Dale).